During the medical check-up of 35 students of a class, their weights were recorded as follows :

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Using points (38,0), (40,3), (42,5), (44,9), (46,14), (48,28), (50, 32) and (52,35), plot a graph.

To find median graphically,

We have total frequency, N = 35

⇒ N/2 = 35/2 = 17.5

Plot 17.5 on the y-axis and draw a horizontal line intersecting the ogive parallel to x-axis.

Observe, from the graph the vertical line parallel to y-axis touches y-axis at 46.5 (approx.).

Hence, median is 46.5.

Finding median by formula:

For median:

We have, total frequency, N = 35

N/2 = 35/2 = 17.5

Observe, cf = 28 is just greater than 17.5.

Thus, median class = 46-48

Median is given by

Where,

L = Lower class limit of median class = 46

N/2 = 17.5

cf = cumulative frequency of the class preceding median class = 14

f = frequency of the median class = 14

h = class interval of the median class = 2

Substituting these values in the formula of median, we get

⇒

⇒ Median = 46 + 0.5

⇒ Median = 46.5

Thus, median is 46.5.

Hence, verified.